This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A072628 #12 Apr 13 2024 05:14:54
%S A072628 1,2,1,2,2,2,2,2,2,4,2,2,2,3,3,3,2,3,2,4,3,4,2,2,3,4,3,4,2,5,2,3,3,4,
%T A072628 4,4,2,3,3,5,2,4,2,4,5,4,2,3,3,6,3,5,2,4,4,5,3,4,2,5,2,3,5,4,4,6,2,4,
%U A072628 3,7,2,4,2,3,5,4,4,6,2,6,4,4,2,5,4,4,3,5,2,7,4,5,3,4,4,4,2,4,5,7,2,5,2,5,7
%N A072628 Number of divisors d of n such that d-1 is not prime.
%H A072628 Amiram Eldar, <a href="/A072628/b072628.txt">Table of n, a(n) for n = 1..10000</a>
%F A072628 a(n) = A000005(n) - A072627(n) < A000005(n).
%e A072628 If n = p is prime then divisors - 1 = {1, p} - 1 = {0, p-1} so a(p) = 2 if p <> 3.
%e A072628 240 has 20 divisors, of them 8 divisors d have nonprime value of d-1, {0, 1, 4, 9, 14, 15, 39, 119}, so a(240) = 8.
%t A072628 di[x_] := Divisors[x]; dp[x_] := Part[di[x], Flatten[Position[PrimeQ[ -1+di[x]], True]]]-1; Table[DivisorSigma[0, w]-Length[dp[w]], {w, 1, 128}]
%t A072628 a[n_] := DivisorSum[n, 1 &, !PrimeQ[#-1] &]; Array[a, 100] (* _Amiram Eldar_, Apr 13 2024 *)
%o A072628 (PARI) a(n) = sumdiv(n, d, !isprime(d-1)); \\ _Amiram Eldar_, Apr 13 2024
%Y A072628 Cf. A000005, A072627.
%K A072628 nonn
%O A072628 1,2
%A A072628 _Labos Elemer_, Jun 28 2002